In seismic exploration for hydrocarbons, AVO (Amplitude-Variation-with-Offset) refers to the variation of P-wave amplitude at increasing shot-to-receiver offset or reflection angle. When rock formations are flat and isotropic (isotropic means that elastic properties of the medium do not change regardless of the directions in which they are measured), reflection amplitude at a fixed offset does not change with the azimuth (direction angle of the shot-to-receiver line measured from the North). This situation is illustrated in FIG. 1a, which shows a seismic ray-path beginning at source (seismic shot point) S, traveling downward to be reflected from a formation surface at D, and then back up to be detected by receiver R. The reflected ray makes an angle θ with the normal to the reflecting surface or to the vertical since the reflector is assumed to be flat. FIG. 1b depicts seismic data recorded by the receiver R for several different values of the source-receiver distance 11 (called the offset), but each reflection event being from the same reflection point D. The receiver measures seismic amplitude as a function of the two-way traveltime for the seismic wave to travel down to D from S and then back up to R (FIG. 1a). The traveltime is related to the depth of the reflection point by the geometry of the ray-path and the seismic wave velocity. The reflector 12 in FIG. 1a is shown in FIG. 1b at different traveltimes (the S-D-R distance), depending on offset. This is because the data have not yet been corrected by a standard seismic data processing procedure called normal moveout.
FIG. 2a illustrates the above-stated definition of azimuth, i.e., the angle ψ between the North direction and the line between the source S and receiver R. FIG. 2b shows a flat response for reflection amplitude as a function of azimuth, which means the medium is azimuthally isotropic. Reflection amplitude, however, becomes azimuthally dependent when the formation beneath the reflection surface is azimuthally anisotropic due to, for example, containing aligned vertical fractures. Reflection amplitude vs. azimuth might then look something like FIG. 2c. In such a case, the amplitude variation is called AzAVO (azimuthal AVO). Geophysicists perform AVO analysis to derive rock and fluid properties of the reservoir formation beneath the reflection boundary. (See, for example, Smith, G. C. and Gidlow, P. M., “Weighted stacking for rock property estimation and detection of gas,” Geophys. Prosp., Eur. Assn. Geosci. Eng., 35, 993-1014 (1987); Rutherford, S. R. and Williams, R. H., “Amplitude-versus-offset variations in gas sands,” Geophysics 54, 680-688 (1989); Castagna, J. P., Swan, H. W., and Foster, D. J., “Framework for AVO gradient and intercept interpretation,” Geophysics 63, 948-956 (1998).) AzAVO data may be inverted to derive rock and fluid as well as fracture properties when fractures are suspected to exist in the reservoir formation, as is disclosed in, for example, Corrigan, D., “The effect of azimuthal anisotropy on the variation of reflectivity with offset: Workshop on Seismic Anisotropy,” Soc. Expl. Geophys., 41WSA, 1645 (1990), and Ruger, A, “Variation of P-wave reflectivity with offset and azimuth in anisotropic media,” Geophysics 63, 935-947 (1998).
AzAVO can also occur when a formation is isotropic but is bounded on top by a dipping boundary surface. This phenomenon may be illustrated by a numerical example. In this synthetic example, seismic lines were shot along many azimuthal directions, as shown in FIG. 3a (angular scale in degrees), over the simple earth model of FIG. 3b. The figure depicts ray-paths from a shot position 31 being detected by many different receivers at 32. Because seismic waves spread out, or diverge, as they travel, divergence corrections are necessary for restoring reflection amplitudes to represent the true reflection strength at the reflection boundary. The state-of-the-art processing, however, does not properly restore amplitudes from dipping reflector because it assumes that rock formations such as 33 in FIG. 3b are flat. It also neglects the amplitude correction for compensating the azimuth-dependent reflection angles. The resultant amplitude, in addition to being offset (or, incident angle) dependent, also becomes azimuthally dependent (FIG. 3c). This illustrates that reflection amplitude at a fixed offset is azimuth dependent when the reflector is dipping. This type of amplitude variation may be called “dip-induced” AzAVO to distinguish it from the AzAVO induced by anisotropy due to, for example, aligned vertical fractures. The dip-induced AzAVO contaminates seismic amplitude not only when formations are isotropic but also when formations are anisotropic.
Quantification and mitigation of dip-induced AzAVO is not commonly done in AVO analysis. This is due not only to negligence but also to the fact that the azimuth information is lost through data processing procedures (e.g., dip-moveout correction and migration). One method, the sector time migration, has been introduced to counter the dip effect for AzAVO inversion. This method first divides the 3-D dataset into many subsets, each containing traces in an angular range about a selected azimuth angle. The subsets are further processed through seismic migration before performing AzAVO analysis. (Seismic migration is a data processing technique that positions reflections at their true locations. The seismic migration is utilized because of variable seismic velocities and dipping horizons.) This method, however, can not fully solve the problem because reflection points are moved different amounts due to the change in apparent dip from sector to sector. Results from time sector migration method may be ambiguous.
Another method in use is the AzAVO inversion of 3-D seismic data without doing seismic migration. This method assumes rock formations are flat, and therefore the divergence correction applied does not compensate the dip-induced AzAVO. The method is preferable to the sector inversion method because it uses amplitude-offset-azimuth information of all traces simultaneously in the inversion to gain statistical power for fracture-attribute estimation. The inversion result, however, may also be ambiguous because the dip-induced AzAVO is not eliminated from the data.
Because oil and gas reservoirs are often not flat, a method to quantify and mitigate the dip-induced AzAVO during seismic-amplitude analysis with or without anisotropy may be beneficial. To increase the reliability of results for both AVO and AzAVO analysis, analytical relationships linking amplitude, dip angle and azimuth angles are beneficial to gain insights, quantify the degree of impact, and design procedures to mitigate the effect. The present invention addresses these needs.